## (1579393975)_{1386}1 is PrP

Expand Messages
• As Phil indicated, it doesn t take much time or brain merely to *find* a PrP of the type that I guess Harvey has in mind to prove. It was as simple as ABC to
Message 1 of 4 , Sep 24, 2001
As Phil indicated, it doesn't take much time or brain merely
to *find* a PrP of the type that I guess Harvey has in mind
to prove. It was as simple as ABC to find

(1579393975)_{1386}1

which is a 13861-digit palindromic PrP,
all of whose digits are odd,
with no neighbouring digits equal
(contrast with top-20 palindromes)

PFGW Version 20010818.Win_Dev
(Beta software, 'caveat utilitor')
Primality testing 15793939750*R(13860)/R(10)+1
[N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file HD13860.fac
Running N-1 test using base 3
Running N-1 test using base 7
Running N-1 test using base 11
Calling Brillhart-Lehmer-Selfridge with factored part 29.59%
15793939750*R(13860)/R(10)+1 is PRP!
(2206.190000 [Rosinante] seconds)

It may be proven prime with 4 more things:
another prime factor of 10^13860-1;
and another (if first less than p57);
a rerun of Pfgw with these factors;
a Konyagin-Pomerance cubic test.

David
• I got trusty old Rosinante to redo all the Pari/Pfgw/Tx tests for the 13861-digit all-odd-digit palindrome (1579393975)_{1386}1 =
Message 2 of 4 , Oct 2, 2001
I got trusty old Rosinante to redo all the Pari/Pfgw/Tx
tests for the 13861-digit all-odd-digit palindrome

(1579393975)_{1386}1 = 15793939750*(10^13860-1)/(10^10-1)+1

and then I packed them in

together with a demo that my Pari KP code replicates
Andy Steward's largest-ever KP test (at 10619 digits).

The KP cubic for the palindrome disagrees with Satoshi's.
But maybe he did not use all the factors?

Satoshi: please check that you ran with
F1=log(F)/log(N)=0.3012668 where F contains
all known prime divisors of N-1.

Did you include repeats,
and also factors of 15793939750?
I did.

David
• David, be glad! I tested using file hd13860p.fac including factors of 15793939750. The result by my program conincides with PARI s output at any point. One of
Message 3 of 4 , Oct 2, 2001

I tested using file hd13860p.fac including factors of 15793939750.
The result by my program conincides with PARI's output at any point.

One of the roots is 3.309279218*10^(-1421).

> Did you include repeats,
> and also factors of 15793939750?
> I did

Yes, previous test didn't use factors of 15793939750.
But it was a 30.05% proof.

Satoshi Tomabechi
• ... I obey:-)
Message 4 of 4 , Oct 2, 2001
Satoshi TOMABECHI commanded: